Consider that the daily standard deviation of the NZX50 index (in New Zealand Dollar, NZD) is 2% and the daily standard deviation of the USD/NZD exchange rate is 1%. Assume that the correlation between the NZX50 and the USD/NZD exchange rate is 0.5 . a. What is the standard deviation of the NZX50 when it is translated to USD? Assume that the USD/NZD exchange rate is expressed as the number of U.S. dollars per one New Zealand Dollar. (Hint: NZX50 in USD = NZX50 in NZD X USD/NZD, hence, the percentage daily change in NZX50 in USD is approximately equal to the percentage daily change in NZX50 in NZD plus the percentage daily change in USD/NZD.) [10 marks] b. Assume that the correlation between the S\&P 500 Index (in USD) and the NZX50 Index (in NZD) is 0.7, the correlation between the S\&P 500 index (in USD) and the USD/NZD exchange rate is 0.3 . The daily standard deviation of the S\&P 500 Index is 1.6%. What is the correlation between the S\&P 500 Index (in USD) and the NZX50 Index when it is translated to USD? (Hint: Let denote the percentage daily change as r, then Covariance (rNZX50 in USD, rS&P in USD )= Covariance (rNZX50inNZD+rUSD/NZD,rS&P in USD ) = Covariance (rNZX50 in NZD, rS&P in USD )+ Covariance (rUSD/NZD,rS&P in USD ). Note that, rNZX50 in USD =rNZX50inNZD+rUSD/NZD is from the Hint in question a). [10 marks]